The equation y = 14x represents the number of pages Printer A can print over time, where y is the number of pages and x is time in minutes. This table shows the number of pages Printer B can print over time.

How many pages does each printer print per minute, and which printer prints at a faster rate?

Select from the drop-down menu to correctly complete the statements.

Printer A prints 
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 pages per minute. Printer B prints 
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 pages per minute. The printer that prints at a faster rate is Printer 
Choose...
.
 
Printer B
Time (min)	Pages Printed
3	48
5	80
8	128
12	192

Let's calculate the rate at which each printer prints pages per minute.

### Printer A:
The equation given is \( y = 14x \), where:
- \( y \) is the number of pages printed.
- \( x \) is the time in minutes.

From this equation, Printer A prints 14 pages per minute, because the coefficient of \( x \) (which is 14) represents the rate.

So, **Printer A prints 14 pages per minute**.

### Printer B:
To find Printer B's printing rate, we need to calculate the number of pages printed per minute from the table.

We will use two points from the table to determine the rate:
- When \( x = 3 \), \( y = 48 \).
- When \( x = 5 \), \( y = 80 \).

Now, calculate the rate of change (pages per minute):
\[
\text{Rate} = \frac{\Delta y}{\Delta x} = \frac{80 - 48}{5 - 3} = \frac{32}{2} = 16 \text{ pages per minute}.
\]
So, **Printer B prints 16 pages per minute**.

### Comparing the rates:
- Printer A prints 14 pages per minute.
- Printer B prints 16 pages per minute.

Thus, **Printer B prints at a faster rate**.

### Final answers:
1. Printer A prints **14** pages per minute.
2. Printer B prints **16** pages per minute.
3. The printer that prints at a faster rate is Printer **B**.

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Would you like more details or have any questions? Here are some related questions to explore:

1. How do you interpret the slope of a linear equation in a real-world context like this one?
2. What would the graph of \( y = 14x \) look like in terms of pages printed over time?
3. How can you calculate the rate of change from a table of values?
4. How would Printer A's rate change if the coefficient in the equation was doubled?
5. What is the significance of the y-intercept in problems like this?

**Tip:** When given data in a table, you can use any two points to calculate the rate of change, which helps in finding the slope for linear relationships.

The equation y = 14x represents the number of pages Printer A can print over time, where y is the number of pages and x is time in minutes. This table shows the number of pages Printer B can print over time. How many pages does each printer print per minute, and which printer prints at a faster rate?

Explore how to compare the printing rates of two printers using linear equations and rate of change. Printer A prints 14 pages per minute, while Printer B prints 16 pages per minute. Find out which printer is faster with this detailed analysis suitable for students in Grades 6-8.

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